Robust Bayesian Synthetic Likelihood via a Semi-Parametric Approach

An, Ziwen; Nott, David J.; Drovandi, Christopher

doi:10.48550/arxiv.1809.05800

Cited by 4 publications

(12 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Everitt (2017) considers a bootstrap approximation to lower the variance of the SL estimator. Furthermore, the normality assumption of SL has also been put under inspection by An et al (2018), which considers a more flexible approximation of the synthetic likelihood using a semi-parametric estimator with a Gaussian copula.…”

Section: ∝ P(y|θ)p(θ)mentioning

confidence: 99%

“…Here we briefly describe the semi-parametric likelihood estimator of An et al (2018), which is aliased as "semiBSL" by the authors. The paper shows examples where BSL fails to produce accurate posterior approximations and provides additional robustness to non-normality of the summary statistics.…”

Section: A Semi-parametric Bsl Likelihood Estimatormentioning

confidence: 99%

“…The choice of the kernel function could be various. An et al (2018) select the Gaussian kernel for simplicity and for its unbounded support.…”

Section: A Semi-parametric Bsl Likelihood Estimatormentioning

confidence: 99%

“…Finally we provide details on obtaining R. With a collection of simulations {η si } n i=1 , it can either be estimated with maximum likelihood estimation, or as An et al (2018) advocate, one could use the Gaussian rank correlation (GRC, Boudt et al (2012)). The GRC estimator is known to be more robust.…”

Section: A Semi-parametric Bsl Likelihood Estimatormentioning

confidence: 99%

“…Here we introduce two shrinkage estimators of the covariance matrix that have shown to be useful in empirical examinations (An et al, 2019;Ong et al, 2018a;An et al, 2018). The shrinkage estimators can be applied to BSL and semiBSL.…”

Section: An Accelerated Likelihood Estimator With Shrinkage Estimationmentioning

confidence: 99%

See 4 more Smart Citations

BSL: An R Package for Efficient Parameter Estimation for Simulation-Based Models via Bayesian Synthetic Likelihood

An¹,

South²,

Drovandi³

2019

Preprint

Self Cite

View full text Add to dashboard Cite

Bayesian synthetic likelihood (BSL) (Price et al., 2018) is a popular method for estimating the parameter posterior distribution for complex statistical models and stochastic processes that possess a computationally intractable likelihood function. Instead of evaluating the likelihood, BSL approximates the likelihood of a judiciously chosen summary statistic of the data via model simulation and density estimation. Compared to alternative methods such as approximate Bayesian computation (ABC), BSL requires little tuning and requires less model simulations than ABC when the chosen summary statistic is high-dimensional. The original synthetic likelihood relies on a multivariate normal approximation of the intractable likelihood, where the mean and covariance are estimated by simulation. An extension of BSL considers replacing the sample covariance with a penalised covariance estimator to reduce the number of required model simulations. Further, a semi-parametric approach has been developed to relax the normality assumption. In this paper, we present an R package called BSL that amalgamates the aforementioned methods and more into a single, easy-to-use and coherent piece of software. The R package also includes several examples to illustrate how to use the package and demonstrate the utility of the methods.

show abstract

Section: ∝ P(y|θ)p(θ)mentioning

confidence: 99%

Section: A Semi-parametric Bsl Likelihood Estimatormentioning

confidence: 99%

“…The choice of the kernel function could be various. An et al (2018) select the Gaussian kernel for simplicity and for its unbounded support.…”

Section: A Semi-parametric Bsl Likelihood Estimatormentioning

confidence: 99%

Section: A Semi-parametric Bsl Likelihood Estimatormentioning

confidence: 99%

Section: An Accelerated Likelihood Estimator With Shrinkage Estimationmentioning

confidence: 99%

See 3 more Smart Citations

BSL: An R Package for Efficient Parameter Estimation for Simulation-Based Models via Bayesian Synthetic Likelihood

An¹,

South²,

Drovandi³

2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

A review of approximate Bayesian computation methods via density estimation: Inference for simulator‐models

Grazian

Fan

2019

WIREs Computational Stats

View full text Add to dashboard Cite

This paper provides a review of Approximate Bayesian Computation (ABC) methods for carrying out Bayesian posterior inference, through the lens of density estimation. We describe several recent algorithms and make connection with traditional approaches. We show advantages and limitations of models based on parametric approaches and we then draw attention to developments in machine learning, which we believe have the potential to make ABC scalable to higher dimensions and may be the future direction for research in this area.

show abstract

Robust Approximate Bayesian Inference with Synthetic Likelihood

Frazier¹,

Drovandi²

2019

Preprint

Self Cite

View full text Add to dashboard Cite

Bayesian synthetic likelihood (BSL) is now an established method for conducting approximate Bayesian inference in models where, due to the intractability of the likelihood function, exact Bayesian approaches are either infeasible or computationally too demanding. Similar to other approximate Bayesian methods, such as the method of approximate Bayesian computation, implicit in the application of BSL is the assumption that the data generating process (DGP) can produce simulated summary statistics that capture the behaviour of the observed summary statistics. We demonstrate that this notion of compatibility between the observed and simulated summaries is critical for the performance of BSL and its variants: across several different simulated and empirical examples, we demonstrate that if the assumed DGP used in BSL differs from the true DGP, BSL can yield unreliable parameter inference. To circumvent this issue, we propose two robust versions of BSL that can deliver reliable inference regardless of whether or not the assumed DGP is correctly specified. Simulation results and two real data examples demonstrate the performance of this robust approach to BSL, and its superiority over standard BSL when the assumed model is misspecified.

show abstract

Robust Bayesian Synthetic Likelihood via a Semi-Parametric Approach

Cited by 4 publications

References 28 publications

BSL: An R Package for Efficient Parameter Estimation for Simulation-Based Models via Bayesian Synthetic Likelihood

BSL: An R Package for Efficient Parameter Estimation for Simulation-Based Models via Bayesian Synthetic Likelihood

A review of approximate Bayesian computation methods via density estimation: Inference for simulator‐models

Robust Approximate Bayesian Inference with Synthetic Likelihood

Contact Info

Product

Resources

About